Optimizing the GRP Scheduling Across the Months


The key task of advertising media planners is to determine the best media schedule of advertising exposures for a certain budget. The planner could choose the media schedule in one of two ways —a continuous strategy or a pulsing strategy. In a continuous strategy the planner schedules advertising more or less even layover all the weeks, so as to be present at all times. In a pulsing strategy the planner advertises in some weeks, often heavily, and not at all in other times. In this pulsing option the media planners hopes that the heavy advertising conducted in one period will be remembered favorably over time, especially at times when making purchase decisions.


This paper offers a methodology that simulates the sales generated through the year using different scheduling strategies and chooses the one which maximizes sales.

Data Requirement

We obtained 30 weeks of data from an FMCG marketer on a monthly basis. The data is as follows:


The first stage in the process is building a robust market mix model. This regression model is essentially an equation that seeks to establish the relationship between sales and the input variables.

Sales = F( Base Sales A + Distribution - Price + TV ad stock +Magazine + Outdoor - Competition TV + Seasonal Effect + error (1)TV here enters as ad-stock and not as spends or GRPs.

This way we incorporate both the carry over effects of advertising and its non linear impact on sales where diminishing returns set in.

We used Vector Auto Regression technique to obtain the parameter estimates, but one can also use OLS or MLE to estimate the parameters. All the parameters were significant individually using the 't' tests. The model was also empirically validates using the Mean Absolute Percentage Error criteria. This model also had business acceptance.

In the second step we use Non Linear Programming (NLP)technique to obtain a GRP schedule that maximizes sales. The market mix equation is treated the objective function in the NLP model. This is exactly the reverse of the regression model. In the regression we provided the GRP every month as ad stock and the regression provided the parameters. In NLP we provide the Beta parameters and the outputs the GRPs. Business constraints include the fact that the overall GRP cannot be exceeded and that there are thresholds and caps on monthly GRP to be deployed.

The Results

Using the estimation method of Congruent Gradient in solving the NLP problem, we obtained a several schedules that maximized the sales. These sales we higher that the obtained sales, week on week. These theoretical sale values had a lift of 2% to 11% over the observed sales, depending on the schedule. Since the algorithm provides multiple solutions it is a call by the media planner to make a choice of the schedule that best meets his requirement. In this case the solution we picked the solution that largely mimicked the original media plan with a higher threshold and lower peaks. This provided a lift of 6% over the observed sales value.

Way Forward

The NLP optimization used a fixed parameter (beta) over the entire period. The optimization will be improved drastically if one were to provide adynamic parameter for TV over time.